Is “Whom did Xun Xi support in the internal turmoil after Duke Xian of Jin's death?” true?

The Records of the Grand Historian, 'Annals of Qin', mentions multiple times that he lived and died with Xi Qi and Zhuo Zi: 'Xun Xi established Zhuo Zi, and Ke again killed Zhuo Zi and Xun Xi.' The Chronicles of the Eastern Zhou Kingdoms, Chapter 28, clearly describes his act of supporting Xi Qi against all objections: 'It is said that Xun Xi supported Prince Xi Qi, and all the officials came to the mourning hall to wail, except Hu Tu, who excused himself on the grounds of serious illness.'